From 6bf4b90c90f15f4ab60833bddf5b5756d1a6b1f6 Mon Sep 17 00:00:00 2001 From: Elizabeth Alexander Hunt Date: Thu, 2 Jul 2026 11:55:17 -0700 Subject: Init --- Homework/math4610/notes/Sep-20.org | 21 +++++++++++++++++++++ 1 file changed, 21 insertions(+) create mode 100644 Homework/math4610/notes/Sep-20.org (limited to 'Homework/math4610/notes/Sep-20.org') diff --git a/Homework/math4610/notes/Sep-20.org b/Homework/math4610/notes/Sep-20.org new file mode 100644 index 0000000..ba067bb --- /dev/null +++ b/Homework/math4610/notes/Sep-20.org @@ -0,0 +1,21 @@ +* Review & Summary +Approx f'(a) with + ++ forward difference $f'(a) \approx \frac{f(a+h) - f(a)}{h}$ + ++ backward difference $f'(a) \approx \frac{f(a) - f(a-h)}{h}$ + ++ central difference $f'(a) \approx \frac{f(a+h) - f(a-h)}{2h}$ + +** Taylor Series +given $C = \frac{1}{2}(|f''(\xi)|) \cdot h^1$ + +with f.d. $e_{\text{abs}} \leq Ch^1$ + +b.d. $e_{\text{abs}} \leq Ch^1$ + +c.d. $e_{\text{abs}} \leq Ch^2$ + +$e_{\text{abs}} \leq Ch^r$ + +$log(e(h)) \leq log(ch^r) = log(C) + log(h^r) = log(C) + rlog(h)$ -- cgit v1.3